Question

Tính: S = 1.2 + 2.3 + 3.4 + ... + 19.20

Answer 1

Ta có:

S=1.2+2.3+3.4+...+19.20

3S=1.2.3+2.3.(4-1)+...+19.20.(21-18)

3S=1.2.3+2.3.4-2.3.1+...+19.20.21-18.19.20

3S=19.20.21=> S=\(\frac{19.20.21}{3}\)= 2660.

Answer 2

S = 1.2 + 2.3 + ... + 19.20

3S = 1.2.(3 - 0) + 2.3.(4 - 1) +...+ 19.20.(21 - 18)

3S = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 +...+ 19.20.21 - 18.19.20

3S = (1.2.3 + 2.3.4 +...+ 19.20.21) - (0.1.2 + 1.2.3 +...+ 18.19.20)

3S = 19.20.21 - 0.1.2

3S = 19.20.21

S = \(\frac{19.20.21}{3}\)

S = 2660